How Many Triangles? 3

Keywords: Starter | Problem Solving | Shape

• B Unit, Texas
• Saturday, February 14, 2009
• "There are 39, not 37"
• Ryan Ames, Edmonton
• Thursday, February 19, 2009
• "I count 51
  Not double counting anything
  and remembering that a triangle is just that three angles in which all angles together equal 180 and there is a bunch in there that are not right angles... Would love to know the correct answer though."
• Ricardo Estopier-Ayala, Strake Jesuit College Prep, Houston, Texas
• Wednesday, March 18, 2009
• "The correct answer is 37 triangles:
  There are:
  12 single triangles
  12 triangles composed of 2 single triangles
  6 triangles composed of 3 single triangles
  6 triangles composed of 4 single triangles and
  1 triangle composed of 6 single triangles.
  
  - The triangles composed of 3 single triangles were the hardest to find, but u can use the giant(composed of 6 single triangles) triangle to find them; they are all contained in it.
  - The triangle composed of 4 single triangles are the same triangles as the ones composed of 3 single triangles, except for the fact that they have just added one triangle to the end.
  - I am unsure how to respond to the person who found 51 triangles other than to say that he/she might have confused the definition of a triangle: A plane geometric figure with three angles and three sides."

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